Large Mimo

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Very Large MIMO Systems:Opportunities and Challenges

Erik G. Larsson

March 21, 2012

Div. of Communication Systems

Dept. of Electrical Engineering (ISY)Linkoping UniversityLinkoping, Sweden

www.commsys.isy.liu.se


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With thanks to my team and collaborators:

Hien Q. Ngo (LiU, Sweden) Antonios Pitarokoilis (LiU) Saif Mohammed (LiU) Daniel Persson (LiU)

Fredrik Rusek (Lund, Sweden)

Ove Edfors (Lund)

Buon Kiong Lau (Lund) Fredrik Tufvesson (Lund)

Thomas L. Marzetta (Bell Labs/Alcatel-Lucent, USA)

Christoph Studer (Rice Univ., USA)

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Erik G. LarssonVery Large MIMO Systems

Communication Systems

Linkoping UniversityMM

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Why MIMO Array gain (beamforming)

Spatial division mult. access

Spatial multiplexing Rate min(nr, nt) log (1 + SNR)

Reliability pe SNRnrnt

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Very Large MIMO

M=

x100

antennas!K

terminals

k=1

k=K

We think of very large (multiuser) MIMO as a system with M K 1 coherent, but simple, processing

Potential to improving rate & reliability dramatically Potential to scaling down TX power drastically

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Large MIMO Arrays

Reduce bulky items (coax) Each antenna unit simple (low accuracy) Resilience against individual failures (hotswapping) Potential economy of scale in manufacturing Enable for mmWave radio (60-300 GHz)?

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Large MIMO: Some Known Facts(Notation: M antennas, K terminals, power per terminal P)

Linear processing (MRC/MRT, ZF, ... ) nearly optimal asM K 1

P and M large enough pilot contamination limitsperformance

Scaling down P with M noise will limit performance.

Perfect CSI & optimal processing P can be scaled as 1/M

Given linear processing and imperfect CSI, in a MU system,P can be scaled as 1/

M

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Large MIMO: Some Known Facts, cont.

System performance can be limited by

intracell interference

pilot contamination thermal noise + intercell interference

so there are several possible operating points depending on

number of antennas available TX power choice of receiver/precoder algorithm coherence time (dictates ultimately the number of users served)

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Large MIMO: Some Beliefs/Speculation

Not enough time for CSI feedback, so must operate in TDD mode. Not enough pilots

Not enough resources for fast CSI feedback System will operate in nearly-noise limited regime (1 bpcu/term)

Very aggressive spatial multiplexing; aggregate efficiency K bpcu Each user could get the full bandwidth simple MAC, little or no control signaling

Impairments, e.g., multiuser interference (almost) drown in noise linear or nearly-linear receivers

May even get away with equalization-free (matched filter only) SCtransmission

Vast excess (M K) of degrees of freedom: use for HW-friendly signal shaping and smart receiver algorithms Per-antenna constant envelope or low-PAR multiuser precoding Channel estimation exploiting subspaces

Channel will harden (random matrix theory) Larger array reveals new propagation phenomena

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Large MIMO: Some of the Most Important Questions

Processing will have to be simple (linear). How good is this?

Non-CSI@TX operation:broadcasting (control signaling) and acquisition

Hardware imperfections: phase noise, I/Q imbalance, A/D, PAs

Synchronization at low SNR

TDD will bring us pilot contamination in the downlink.How bad is this really in practice?

TDD will require reciprocity calibration.

How, when and at what cost?

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Favorable Propagation andIts Implications

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Communication SystemsLinkoping University

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Favorable propagation and Rate Consider M K, MIMO link, channel H, M K. Rate:

R =

K

k=1

log21 +

SNR

K2

k , SNR =Ptot

N0

If |Hij | 1,K

k=1 2k = H2 M K, so

log2 (1 + MSNR)

rank-1 channel (LoS)21=MK, 2

2==2

K=0

R K log2

1 +M

KSNR

HHHI (full rank channel)

21==

2

K=M

Favorable propagation

H i.i.d. and M K favorable propagation. In MU-MIMO (H G), favorable propagation if

GHG

M

1 0 00 2

. . ....

.... . .

. . . 00 0 K

D, M K10/29



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Favorable propagation and ideal channels

40 30 20 10 0 10 20 300

0.1

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1

Prob(

a

bscissa)

ordered singular values [dB]

i.i.d 6x128

i.i.d. 6x6

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Do we have favorable propagation in practice?

Our partners at Lund Univ., Sweden have conducted uniquemeasurements [RPL2011+,GERT2011].

Indoor 128-ant. (4x16 dual-pol.) array. 3 users indoor, 3 outdoor.

2.6 GHz CF, 50 MHz BW, 100 snapshots (10m).

Normalized to retain only small-scale fading.

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Lund measurements, example of results

40 30 20 10 0 10 20 300

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0.2

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0.5

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0.7

0.8

0.9

1

Prob(

a

bscissa)

ordered singular values [dB]

meas 6x128

meas 6x6

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Spectral/energy efficiency tradeoffs

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Uplink single-cell, model assumptions

gk =

khk. hk: small scale fading;

E[|hmk|2] = 1; zero mean. k: path loss+shadowing SNR for kth terminal: P k

RX signal:

y =

P

Kk=1

gk

M1

xk +n, E[|xk|2] = 1, ni CN(0, 1)

Write as

y =

P GMK

xK1

+n, G = HD1/2, H [h1, . . . ,hK], D

1. . .

K

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Spectral-energy efficiency tradeoff Sum-spectral efficiency:

R = 1 T

Klog2 1 + (M1)P

2

(K1)P2+(+K)P+1, for MRC

1 TKlog2 1 + (MK)P2(+K)P+1 , for ZF Energy efficiency: =

R

P Reference mode: K= 1,M= 1

arg max1T Single-user system: K= 1,M fixed

arg maxP,

, s.t. S= const., 1 T

Multi-user system: M fixed

arg maxP,K,

s.t. S= const.,K T(KM for ZF) 16/29



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C ( ) [ ]


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Cellular UL, (BT)coh. = 14 14, M = 1 [NLM2011]

0 10 20 30 40 50 60 70 80 9010

-1

100

101

102

103

104

K=1, M=1

20 dB

10 dB

0 dB

-10 dB

Re

lativeEnergy-Efficiency(bits/J)/(bits/J)

Spectral-Efficiency (bits/s/Hz)17/29



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C ll l UL (BT ) 14 14 M 100 [NLM2011]


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0 10 20 30 40 50 60 70 80 9010

-1

100

101

102

103

104

K=1, M=1

20 dB

10 dB

0 dB

-10 dB

Re


Spectral-Efficiency (bits/s/Hz)

K=1, M=100

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C ll l UL (BT ) 14 14 M 100 [NLM2011]


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0 10 20 30 40 50 60 70 80 9010

-1

100

101

102

103

104

K=1, M=1

MRC

20 dB

10 dB

0 dB

-10 dB

-20 dB

Re



K=1, M=100

M= 100

ZF

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C ll l UL (BT ) 14 14 M 50 [NLM2011]


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0 10 20 30 40 50 60 70 80 9010

-1

100

101

102

103

104

-20 dB

M=50

ZF

MRC

20 dB

10 dB

0 dB

-10 dB

RelativeEnergy-Efficiency(bits/J)/(bit

s/J)


K=1, M=50

K=1, M=1

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Erik G. LarssonVery Large MIMO SystemsCommunication Systems


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Large-Scale MU-MIMO

Downlink Precoding

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Erik G. LarssonVery Large MIMO Systems Communication SystemsLinkoping University MM

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D li k di g g l ks


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Downlink precoding - general remarks

In the downlink, the are M K unused degrees of freedom.These excess DoF could be used to Null out interference Shape the transmitted signals in a hardware-friendly way

An excess in the number of antennas also means that simpleprecoders (MRT, time-reversal) may be used to combat frequencyselectivity

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Constant Envelope MU MIMO Downlink Precoding


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Constant Envelope MU-MIMO Downlink Precoding

Constant-envelope transmission [SM2011a,SM2011b]

x =

P

M

ej1

...ejM

Insensitive to PA non-linearity.

How well can we approximate a desired wavefield at K locations, byvarying only the phase of the transmitted signals?

Not to be confused with equal-gain transmission (something entirelydifferent)!

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Constant Envelope versus Beamforming


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Constant Envelope versus Beamforming

u

P

h1

h

P

hm

h

P h

Mh

Amplitude range = [0

P|u|]

eju

1

eju

m

eju

M

Constant amplitude =

PM

PM

PM

PM

Antenna 1 Antenna 1

Antenna m Antenna m

Antenna M Antenna M

Beamforming Constant-envelope transmission

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Constant env MU MIMO precoding Gauss symbols


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Constant-env. MU-MIMO precoding, Gauss. symbols

0 50 100 150 200 250 30012

9

6

3

0

3

6

9

12

1515

No. of Base Station Antennas (M)

Min.reqd.

PT

/2

(dB)toachiev

eaperuserrateof

2bpcu

K = 10, Proposed CE Precoder (CE)

K = 10, ZF Phaseonly Precoder (CE)

K = 10, GBC Sum Cap. Upp. Bou. (APC)

K = 40, Proposed CE Precoder (CE)

K = 40, ZF Phaseonly Precoder (CE)

K = 40, GBC Sum Cap. Upp. Bou. (APC)

1.7 dB

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PAR Aware MU MIMO OFDM Downlink [SL2012]


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PAR-Aware MU-MIMO OFDM Downlink [SL2012]

Precoder design problem:

(PMP) minimizea1,...,aN

maxa1 , . . . , aNsubject to sw = Hwfw(a1, . . . , aN), w T0N1 = fw(a1, . . . , aN), w Tc.

Hw: time-frequency channel

fw(

) linear function; includes OFDM modulation and S/P

conversion T: used subcarriers; Tc: null subcarriers Convex optimization problem, fast algorithm; relaxation

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PAR-aware MU-MIMO OFDM DL (99% percentiles)


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PAR-aware MU-MIMO OFDM DL (99% percentiles)

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Literature


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LiteratureRPL+2011 F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L.

Marzetta, O. Edfors, and F. Tufvesson, Scaling up MIMO:Opportunities and Challenges with Large Arrays,arXiv:1201.3210, 2011.

NLM2011 H.Q. Ngo, E.G. Larsson and T. Marzetta, Energy andSpectral Efficiency of Very Large Multiuser MIMOSystems, arXiv:1112.3810, 2011.

LM2011a E.G. Larsson and S.K. Mohammed, Per-antenna ConstantEnvelope Precoding for Large Multi-User MIMO Systems,arXiv:1201.1634v1, 2011.

LM2011b E.G. Larsson and S.K. Mohammed, Single-UserBeamforming in Large-Scale MISO Systems...: TheDoughnut Channel, arXiv:1111.3752, 2011.

SL2012 C. Studer and E.G. Larsson, PAR-Aware Large-ScaleMulti-User MIMO-OFDM Downlink, arXiv:1202.4034,2012.

HBD2011 J. Hoydis, S. ten Brink, M. Debbah, Massive MIMO: HowMany Antennas do We Need?, arXiv:1107.1709, 2011.GERT2011 X. Gao, O. Edfors, F. Rusek, and F. Tufvesson, Linear

pre-coding p erformance in measured very-large MIMOchannels, IEEE VTC 2011

Mar2010 T. L. Marzetta, Noncooperative MU-MIMO with unlimitednumbers of base station antennas, IEEE Trans. Wireless.Comm. 2010.

JAMV2011 J. Jose, A. Ashikhmin, T. L. Marzetta, and S. Vishwanath,Pilot contamination and precoding in multi-cell TDDsystems, IEEE Trans. Wireless Commun., 2011.

GJ2011 B. Gopalakrishnan and N. Jindal, An Analysis of PilotContamination on Multi-User MIMO Cellular Systems withMany Antennas, IEEE SPAWC 2011.

NML2011 H. Q. Ngo, T. Marzetta and E. G. Larsson, Analysis of thepilot contamination effect in very large multicell multiuser

MIMO systems for physical channel models, IEEE ICASSP2011.

PML2012 A. Pitarokoilis, S. K. Mohammed and E. G. Larsson, Onthe optimality of single-carrier transmission in large scaleantenna systems, IEEE Wireless Communication Letters,submitted, 2012.

CMT2004 G. Caire, R. Muller and T. Tanaka, Iterative multiuserjoint decoding: optimal power allocation and low-complexityimplementation, IEEE Trans. IT, 2004.

ZLW2007 H. Zhao, H. Long and W. Wang, Tabu search detection forMIMO systems, IEEE PIMRC 2007.

VMCR2008 K. Vishnu Vardhan, S. Mohammed, A. Chockalingam, andB. Sundar Rajan, A low-complexity detector for largeMIMO systems and multicarrier CDMA systems, IEEEJSAC 2008.

Sun2009 Y. Sun, A family of likelihood ascent search multiuserdetectors: an upper bound of bit error rate and a lowerbound of asymptotic multiuser efficiency, IEEE JSAC 2009.

LH1999 A. Lampe and J. Huber, On improved multiuser detectionwith iterated soft decision interference cancellation, inProc. IEEE Communication Theory Mini-Conference, 1999.

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Thank You

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